A gait is a way of walking, either an individual’s particular way of moving from one place to another, or an animal’s pace of moving, such as a trot, gallop, or canter. It can be used as a verb to train an animal to walk a certain way.
Incidentally gait did come from gate, which meant way. While gate, which is an opening in a barrier, usually a fence, came from the Norse gat, which meant opening.
Gate can also be a verb, meaning to put a gate in something. In Britain it can mean to lock down a university or dorm.